Angle dependent surface multiple attenuation for two-component marine bottom sensor data

ABSTRACT

A method of processing data that uses an angle dependent filter from two-component sensor data may allow for attenuation of free surface multiples. Typically, the sensors that are used to produce two-component ocean bottom sensor data are hydrophones and geophones. The method decomposes the recorded dual sensor data into upgoing and downgoing wavefields by combining the recorded pressure at the hydrophone with the vertical particle velocity from the geophone recorded at the ocean floor. Surface multiple attenuation is accomplished by application of an incident angle dependent deconvolution of the downgoing wavefield from the upgoing wavefield. The method uses an angle dependent filter to calibrate the geophone response so that the different coupling of the two instruments and associated noise are taken into account.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention generally relates to marine seismic exploration, and more particularly to a marine seismic measurement system that allows for attenuation of free surface multiples in two-component marine bottom sensor data.

[0003] 2. Description of the Relevant Art

[0004] Marine seismic wave measurement systems may be used to take seismic profiles of underwater geologic configurations. One procedure of marine seismic measurement involves the use of a marine bottom cable. Surveys using marine bottom cables are often employed in areas that are populated with numerous obstacles, such as drilling and production platforms. In a procedure using marine bottom cable, several miles of bottom cables may be deployed along the marine bottom. Often, multiple cables are deployed in parallel. Each bottom cable may have a plurality of sensor pairs placed at regular intervals along the cable. Each sensor pair may contain a pressure sensor, such as a hydrophone, and a particle velocity sensor, such as a geophone. A gimbal mechanism within each geophone ensures that the sensing elements of the geophones are vertically oriented.

[0005] Acoustic energy is generated in the vicinity of the marine bottom cables using an acoustic energy source such as an air gun array or a marine vibrator array. An air gun discharges air under very high pressure into the water. Marine vibrators typically include a pneumatic or hydraulic actuator that causes an acoustic piston to vibrate at a range of selected frequencies. The vibrations of the acoustic vibrator produce pressure differentials in the water that generate acoustical energy pulses. Source acoustical waves travel downward through the water and into the earth as seismic waves. The source waves may strike interfaces between formations in the earth. A portion of the source wave may be reflected upwards from the interface towards the marine bottom. The sensor array on the marine bottom receives the reflected waves and converts the waves into signals that are recorded as sensor data. The sensor data may be processed to provide information about the structure of the formations beneath the marine bottom.

[0006] The sensor array receives not only the reflected waves of interest, but also the source waves and reverberated waves. Reverberated waves are waves that have been reflected from the water-air interface back towards the marine bottom. Such reverberated waves may be referred to as free surface multiples or surface multiples. The free surface multiples may be significant in amplitude and may be difficult to differentiate from the desired reflected waves.

[0007] The use of dual sensor measurements, namely pressure and vertical particle velocity, may allow for the attenuation of free surface multiples. U.S. Pat. Nos. 5,163,028; 5,365,492; 5,524,100, and 5,621,700 describe methods of attenuating free surface multiples, and each of these patents are incorporated by reference as if fully set forth herein. The methods of attenuating free surface multiples detailed in the above referenced patents do not adequately take into consideration the angle dependence of the upgoing and downgoing wavefields. Also, the methods of attenuating multiples detailed in the above referenced patents do not adequately take into consideration the angle dependency of the response of each sensor of a sensor pair. The use of methods of attenuating of multiples that do not consider both the angle dependency of the upgoing and downgoing wavefields and the angle dependency of the response of each sensor of a sensor pair may lead to inaccurate determinations of the formations present beneath the marine bottom.

[0008] Existing methods of deconvolution for multiple attenuation of dual sensor data carry out the calibration and deconvolution filter in the offset distance-time domain, (x,t). The basic equations for deconvolution of upgoing and downgoing waves are valid only in the angle (plane wave) domain. Seismograms recorded from a single shot will have energy propagating at all possible angles, so processing data in the offset distance-time domain can only have limited success.

SUMMARY OF THE INVENTION

[0009] The problems outlined above may in large part be solved by a system and method of marine seismic exploration that takes into account angle dependencies during processing of two-component sensor data. Consideration of angle dependencies of upgoing and downgoing wavefields, as well as the angle dependencies of the sensors, may enhance the attenuation of free surface multiples that are present in two-component sensor data. The ability to provide enhanced attenuation of free surface multiples may allow for more accurate determination of the formations present beneath a marine bottom.

[0010] In an embodiment, a method is used to decompose the recorded dual sensor data into upgoing and downgoing wavefields. The method finds an angle dependent calibration factor that allows the calibration of the recorded pressure data with respect to the recorded vertical particle velocity data Alternatively, the method finds an angle dependent calibration factor that allows the calibration of the recorded vertical particle velocity data with respect to the recorded pressure data. The angle dependent calibration factor may take into consideration the angle dependencies of the hydrophone and the geophone, as well as noise associated with the recording geometry. Attenuation of multiples may be accomplished by application of an incident angle dependent deconvolution of the downgoing wavefield from the upgoing wavefield calculated from the calibrated pressure and vertical particle velocity data.

BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Further advantages of the present invention will become apparent to those skilled in the art with the benefit of the following detailed description of embodiments and upon reference to the accompanying drawings in which:

[0012]FIG. 1 is an illustration of a marine seisnic survey system;

[0013]FIG. 2 is an illustration of a primary wave impinging a sensor pair;

[0014]FIG. 3 is a flow diagram representing a method of processing marine seismic survey data that takes into consideration the angle dependency of sensor response and the angle dependency of the upgoing and downgoing wavefields;

[0015]FIGS. 4a and 4 b show pressure and vertical velocity data, respectively, from synthetic shot data for a 1-D four layer model;

[0016]FIGS. 5a and 5 b show the data represented in FIGS. 4a and 4 b transformed to the plane wave domain;

[0017]FIGS. 6a and 6 b show the calculated separated upgoing wavefield and the corresponding calculated downgoing wavefield, respectively.

[0018]FIG. 7a shows the multiple attenuation result in the offset distance-time domain;

[0019]FIG. 7b shows the location of the simulated primaries of the model;

[0020]FIG. 8 shows hydrophone data from an offshore ocean bottom experiment in the South China Sea;

[0021]FIG. 9 shows corresponding geophone data for the ocean bottom experiment in the South China Sea depicted in FIG. 8; and

[0022]FIG. 10 shows the multiple attenuation result obtained after processing the data represented in FIGS. 8 and 9.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0023] With reference to the drawings, and particularly to FIG. 1, a marine seismic survey system is generally designated by reference numeral 10. The system 10 may include a seismic survey ship 12 that tows an acoustic energy source 14 through a body of water 16. The acoustic energy source may be an array of acoustic energy sources. Each acoustic energy source may be an air gun, a marine vibrator, or another device that generates acoustic waves. The construction and operation of acoustical energy sources is well known in the art and is not described in detail herein. The activation of the acoustic energy source is referred to as “shooting.”

[0024] The system 10 may also include receiving ship 18. The receiving ship 18 deploys bottom cable 20 on marine bottom 22. The receiving ship may deploy an array of bottom cables in parallel lines. Each bottom cable 20 carries at least one sensor pair 24, and preferably, each bottom cable carries a plurality of sensor pairs. Each sensor pair 24 may include a pressure sensing transducer, such as a hydrophone, and a particle velocity sensor, such as a geophone. As is well known in the art, each marine geophone may include a gimbal mechanism to ensure that the sensing element of the geophone is vertically oriented during use. Each hydrophone and geophone may send separate data signals to the receiving ship 18. The data may be recorded by a multi-channel seismic recording system that selectively amplifies, conditions and records time-varying electrical signals. The system may also digitize the received signals to facilitate signal analysis. Any of a variety of seismic recording systems may be used to record the data.

[0025] To take a marine seismic survey, the receiver ship 18 positions the bottom cable 20 on the marine bottom 22. In an embodiment, shooting takes place while the survey ship 12 moves at a constant speed along a set of survey lines with respect to the cable 20. The location and depth of each sensor pair 24, and the location of the acoustical energy source 14 at the time of each shot are recorded. After the survey ship 12 completes the survey line, the receiving ship 18 retrieves the cable 20 and re-deploys the cable in a new position. After re-deployment of the cable 20, the survey ship 12 may shoot another set of survey lines.

[0026] During data collection, seismic waves 26 generated by the source 14 travel away from the source. Portions of the waves travel downward and into the land beneath the marine bottom 22. The waves may be reflected off of interfaces between subterranean formations, such as interface 28 between subterranean formations 30 and 32 as shown in FIG. 1. Reflected waves 34 from the interfaces may travel upwards and impinge upon a sensor pair 24. The sensor pairs 24 detect the reflected waves 34 and transmit signals along the cable 20 to the receiving ship 18. The receiving ship I 8 records the data so that the data can be subsequently processed to map the location of interfaces 28 between subterranean formations.

[0027] The sensor pairs 24 receive not only the reflected waves 34, which are also known as primaries, but also the source waves 26 and free surface multiples 36. The free surface multiples 36 may be significant in amplitude and may be difficult to differentiate from the desired reflected waves 34. Free surface multiples that originate from the source, contact the air/surface interface 38, and travel towards the marine bottom are referred to as ghosts 40.

[0028] In marine seismic data acquisition, the energy source 14 is always placed above the marine bottom 22. All upgoing wavefields in the data result from reflections of downgoing incident waves to the marine bottom. Mathematically, this is formulated by the following convolution,

d(t)^(up) =r(t){circle over (×)}d(t)^(dn)  (1)

[0029] where d(t)^(up) are the upgoing wavefields, which can be either primaries 34 or multiples 36; and d(t)^(dn) is the downgoing wavefield, which may be direct transmission from the source 26 or reflection events 36 (source, primaries or multiples) that are bounced back at the air/surface interface 38 (receiver ghosts). In equation (1), r(t) is the reflectivity of the structure, which includes those reflections taking place both at the marine bottom 22 and inside the land structure below the marine bottom; and t is the wavefield traveltime. The reflectivity, r(t), also includes internal multiple reflections.

[0030] The reflectivity, r, may be obtained by deconvolving the downgoing wavefield from the upgoing wavefield. In the frequency domain, this may be represented by a simple division:

R(ω)=D(ω)^(up) /D(ω)^(dn)  (2)

[0031] where R(ω), D(ω)^(up), and D(ω)^(dn) are the Fourier transforms with respect to time of r(t), d(t)^(up), and d(t)^(dn), respectively.

[0032] The deconvolution based multiple attenuation method given in equation (2) requires separated upgoing and downgoing wavefields. The upgoing and downgoing wavefields may be represented by the upgoing and downgoing pressure, or by the upgoing and downgoing vertical particle velocity.

[0033] In the above description, the angle dependency of the propagating waves was suppressed to present the fundamental ideas behind processing two-component marine bottom sensor data. The development below takes into account angle dependence.

[0034] Seismic data are recorded in the offset distance-time domain. Offset distance is the horizontal distance between the location of a sensor pair 24 and the location of the acoustic energy source 14 at the time of a shot. The seismic data recorded by a sensor pair 24 may be a record of the variation in pressure, as measured by hydrophones, and vertical particle velocity, as measured by geophones, taken as a function of source-to-receiver offset distance and time. The acoustic energy source 14 may be considered to be a point source. In practice, the source 14 will have a directivity that is angle dependent. The response of a source can be synthesized by summing the responses from a series of plane waves each characterized by the propagation angle of the plane wave. The source generated data recorded in the offset-time domain may be decomposed into plane waves by means of a Radon transform. If u(x,ω) are the recorded data where x is the vector representing the source-to-receiver offset distance, and ω is the frequency, the plane wave response may be given by:

u (τ, p )=∫dω∫dx u(ω, p )e ^(−iω(t−p·x))

[0035] where p is the vector ray-parameter, and τ is the offset time, or τ=t−p·x. In a two-dimensional geometry, p=p_(x)=p=sinθ/α. The angle θ is the angle of propagation, and α is the velocity of sound in the medium. The angle of propagation θ is illustrated in FIG. 2 for a primary wave 34.

[0036] In the frequency-ray-parameter domain, the pressure recorded by hydrophones may be given by the equation:

P(ω,p)=c ₁(p)(1+R(ω,p))⁻¹(e ^(−iωqh) +R(ω,p)e ^(−ωqh))S(ω,p)  (3)

[0037] The corresponding vertical velocity geophone data in the frequency-ray parameter domain may be given by the equation:

V _(z)(ω,p)=c ₂(p)(1+R(ω,p))⁻¹(R(ω,p)^(−iωqh) −e ^(−iωqh))S(ω,p)  (4)

[0038] where p is the ray-parameter; θ is the angle of propagation; α is the sound velocity in the medium; R is the reflectivity of the structure referenced to the water surface, which includes the response of both the primaries and internal multiples; h_(r) is the receiver depth; q is the vertical slowness, or q=((1/α²−p²))^(½)); S is the source wavelet with source side ghosts; and c₁ and c₂ are two incident angle dependent coefficients defined by the ray-parameter and the parameters of the medium.

[0039] The upgoing and downgoing wavefields may be obtained by combining the pressure and the vertical components of the vertical particle velocities in equations (3) and (4) to yield:

P(p)^(up)=(½)(P(p)+c(p)V _(z)(p)), P(p)^(dn)=(½)(P(p)−c(p)V _(z)(p))  (5)

[0040] where c(p) is a function defined by the parameters of the medium.

[0041] Equation (5) may be considered to be an equation describing a system wherein the hydrophones and the geophones are perfectly coupled to the environment, wherein the hydrophones and the geophones have the same response characteristics, and wherein the environment surrounding the sensor pair 24 is noise free. Direct application of Equation (5) may not yield good results because, in reality, a sensor pair is not perfectly coupled to the environment, the instrument response characteristics of hydrophones and geophones are not the same, and sensor pairs 24 are not located in noise free environments. The angle dependency of the sensor pairs may require that the geophone data be calibrated to the pressure data, or vice versa, before the upgoing and downgoing wave components are determined.

[0042] From equations (3) and (4), the following equation may be derived:

Ŝ(ω,p)=(½)[(1+Z(ω,p))]P(ω,p)[(1−Z(ω,p))]V _(z)(ω,p)  (6)

[0043] Where Z(ω,p) is a filter and Ŝ(ω,p) is the temporal Fourier transform of the time delayed source function, which is a function of the source excitation function S(ω,p), and may be given by the equation:

Ŝ(ω,p)=(1/(2qα ²))e ^(−iωqh)(e ^(−iωqh) −e ^(−iωqh) S((ω,p))

[0044] The term Ŝ(ω,p) contains the source excitation function S(ω,p), the source side ghosts and the transmission operator.

[0045] Since the source excitation function is always of finite duration in real data, there must exist a time T₀(p), such that:

ŝ(t,p)=0, if t>t ₀ +h _(r)/α(  (7)

[0046] where ŝ(t,p) is the inverse temporal Fourier transform of Ŝ(ω,p), which is the delayed source function.

[0047] Equation (7) may allow the hydrophone data and the geophone data to be calibrated so that the delayed source function is optimal. The calibration filter may be designed such that the delayed source function defined in equation (7) will have minimum energy after a certain time. The time will include the source excitation function time duration and the sum of the propagation time of the energy of the source to go to the receiver and back to the surface. The calibration function, ƒ(ω,p), may be found by solving the following equation and constraint:

||F ⁻¹[(1+Z(ω,p)) P(ω,p)+ƒ(ω,p) (1−Z(ω,p))]V _(z)(ω,p)||=minimum  (8)

t>T ₀ =t ₀ +h _(r)/α

[0048] where F⁻¹ stands for the inverse Fourier transform operator. A numerical method of solving for the calibration function in a least squares sense may involve solving a system of equations with Toepliz structure to find a value for the calibration function for a given value of p. A person having ordinary skill in the art will recognize many methods may be used to solve the equation and constraint of Equation (8) to yield the optimum angle dependent calibration function.

[0049] Finding the calibration function allows for the calibration of hydrophone and geophone data. Angle dependent multiple attenuated data may then be obtained by forming and using an optimal filter from the calibrated data by application of Equations (5) and (2).

[0050] The methodology for processing two-component marine sensor data is shown diagrammatically in FIG. 3. FIG. 3 shows that the data is first collected and recorded in the offset distance—time domain. The data is then transformed to the plane wave domain, τ−p. Each p trace of the transformed data set may be converted into multiple free data by the application of the steps illustrated within block 42. For each p trace of the transformed data set, a calibration function is numerically calculated based on Equation (8). The calibration function is then used to calibrate the vertical particle velocity data with respect to the pressure data. The calibrated data is then used to find information corresponding to the upgoing and downgoing wavefields. The upgoing and downgoing wavefield information is used to numerically solve for an optimal filter to suppress multiples by applying Equation (2). The optimal filter for the p trace is then used to generate multiple free data for the p trace. The generated multiple free data for each p trace forms a multiple free data set. The multiple free data set may be transformed back to the offset—time domain.

[0051] FIGS. 4-7 show a theoretical application of the method of processing two-component marine seismic data to a 1-D four layer acoustic model. The hydrophone and geophone data are shown in FIGS. 4a and 4 b. FIGS. 5a and 5 b show the τ−p transformation of the data. The pressure shown in FIG. 5b is then decomposed into an angle dependent estimate of the upgoing wavefield and the downgoing wavefield by applying equation (5). The upgoing wavefield is shown in FIG. 6a, and the downgoing wavefield is shown in FIG. 6b. The reflectivity of the model is computed by deconvolving the downgoing wavefield from the upgoing wavefield in the τ−p domain. Following an inverse τ−p transform, the final result in τ−p domain is obtained and shown in FIG. 7a. By comparing the results shown in FIG. 7a with the original data sets shown in FIGS. 4a and 4 b, and with the simulated primary reflections of the model as shown in FIG. 7b, it may be seen that the method of processing two-component marine seismic data attenuates the multiples in the data and recovers the reflectivity of the model. In FIGS. 4-7, the arrows point out the location of the three primary interfaces, which represent the water-land interface, and two subterranean interfaces.

[0052] The method has also been applied to ocean bottom dual sensor data collected in the South China Sea. FIG. 8 shows the pressure data, and FIG. 9 shows the corresponding vertical particle velocity. After transforming into the plane wave domain, the geophone data are calibrated before separating the upgoing and downgoing wavefields. The final result of multiple attenuation is shown in FIG. 10. For comparison with the original data, the result has been convolved with a zero phase wavelet derived from the autocorrelation of each p trace in the hydrophone data before inverse τ−p transform. As shown in FIG. 10, the multiples have been attenuated, and more importantly, the primary reflections, which are marked by arrows, have been preserved. The primary reflections were not strongly visible in the original data due to the presence of strong multiples.

[0053] Further modifications and alternative embodiments of various aspects of the invention will be apparent to those skilled in the art in view of this description. Accordingly, this description is to be construed as illustrative only and is for the purpose of teaching those skilled in the art the general manner of carrying out the invention. It is to be understood that the forms of the invention shown and described herein are to be taken as examples of embodiments. Elements and materials may be substituted for those illustrated and described herein, parts and processes may be reversed, and certain features of the invention may be utilized independently, all as would be apparent to one skilled in the art after having the benefit of this description of the invention. Changes may be made in the elements described herein without departing from the spirit and scope of the invention as described in the following claims. 

What is claimed is:
 1. A method for attenuation of multiples in marine seismic data, comprising: creating seismic wavefields in a water environment, each created wavefield generated at a different location; recording sensor readings from at least one sensor pair, wherein said at least one sensor pair comprises two different types of sensors, wherein said sensor readings are substantially a result of the created seismic wavefields, and wherein said sensor reading form a data set; calculating angle dependent estimated values for upgoing and downgoing wavefields that generated the data set; and generating an attenuated multiple data set using the estimated values for the upgoing and downgoing wavefields.
 2. The method as defined in claim 1, wherein the at least one sensor pair comprises a pressure sensor and a vertical particle velocity sensor.
 3. The method as defined in claim 1, wherein calculating angle dependent estimated values for upgoing and downgoing wavefields further comprises: transforming the data set to a plane wave domain data set; calibrating the plane wave domain data set using angle dependent calibration functions; and using the calibrated plane wave domain set to calculate the estimated values for the angle dependent upgoing and downgoing wavefields.
 4. A system for generating attenuated multiple data for two-component marine seismic sensor data, comprising: an acoustic energy source configured to generate an acoustic wavefield; at least one sensor pair, the at least one sensor pair comprising two types of sensors configured to detect wavefields resulting from the generation of an acoustic wavefield by the acoustic energy source; a recording system configured to separately record sensor readings from each sensor of the at least one sensor pair as data, the recording system configured to record the location of the acoustic energy source at a time when the acoustic energy source generates an acoustic wavefield, and said recording system configured to record the location of the at least one sensor pair; and a data processor configured to analyze the data and produce the attenuated multiple data; wherein the data processor calculates angle dependent estimated values of upgoing and downgoing wavefields that generated the data set, and wherein the data processor uses the estimated values of the upgoing and downgoing wavefields to generate the attenuated multiple data during use.
 5. A method of generating attenuated multiple data from two-component marine seismic data, comprising: calculating angle dependent estimated values for upgoing wavefields and downgoing wavefields that generated the data; and generating an attenuated multiple data set using the estimated values for the upgoing and downgoing wavefields. 